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    Leibniz equivalence, which dissolves hole-type indetermin... — Carmelics
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    Challenges→Separating space-time structures into manifold and metric opens up problems for determinism beyond the hole argument

    Leibniz equivalence, which dissolves hole-type indeterminism by identifying diffeomorphic models, is compatible with retaining the manifold-metric distinction.

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    1 reason for
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    Reasons For

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    Reason for
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    • 1.Diffeomorphic models represent identical physical possibilities, so identifying them preserves empirical content while eliminating spurious indeterminism.
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    • 2.The manifold provides the topological structure needed for physics; the metric encodes physical geometry. These are conceptually distinct but jointly necessary.
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    • 3.Leibniz equivalence respects the principle that unobservable differences shouldn't multiply ontological commitments or generate determinism failures.
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    Reasons Against

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    Reason against
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    • 1.If manifold and metric are truly distinct, diffeomorphisms that preserve metric structure may not preserve all physically meaningful properties of the manifold.
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    • 2.Leibniz equivalence assumes observational indistinguishability entails metaphysical identity, but this conflates epistemology with ontology illegitimately.
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    • 3.Retaining the manifold-metric distinction while eliminating diffeomorphic models creates tension: one entity (manifold) seems underdetermined by physics independently.
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    Related

    Diffeomorphic models represent identical physical possibilities, so identifying ...If manifold and metric are truly distinct, diffeomorphisms that preserve metric ...Leibniz equivalence assumes observational indistinguishability entails metaphysi...Leibniz equivalence respects the principle that unobservable differences shouldn...
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    Retaining the manifold-metric distinction while eliminating diffeomorphic models...Separating space-time structures into manifold and metric opens up problems for ...The manifold provides the topological structure needed for physics; the metric e...

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